I grew up just north of Annapolis, Maryland which has high heat and humidity in the summers. Our house was built in about 1770 (yes, before the Constitution was written). (The basement was made of boulders and the kitchen was originally a separate building as they burned down all the time.). Our house did have one little air window conditioning unit which barely cooled one room in our large house and that I don't recall that we used much, so we effectively had no air conditioning. I scanned these comments to see if someone else recommended the same set up as our house in Maryland and I do not see it, so here it is.
Our building is three stories tall with a big central staircase. You use the top floor for bedrooms and in the morning (1) open the windows and (2) leave for the rest of the day. What happens is that the top floor gets really hot from the sun, and then the air goes up, which means it goes out the windows. That creates a vacuum which pulls air up the staircase and which then pulls air in the windows of the lower floors where people are during the day. This creates a constant stream of moving air which cools people down wonderfully. The effect is amplified if the second story has shut windows as the flow of the air must all come in the ground floor and the flow at that floor is therefore increased. Seems to work best if there are lots of windows on the lower floor and somehow (I know not how) seems to work better if the building is made of wood. Basically the whole building was a passive heat engine that turned on automatically when you needed it and turned off automatically when you did not. Very elegant and efficient.
People also used to cut ice from lakes in the winter and store it in special ice houses which were designed deliberately as above, but since they were special-purpose buildings, they could be engineered to be even more efficient. If I recall correctly, there would be just a tower with no internal "floors" at all (a huge "staircase") and the middle "floor" would have no windows at all. The outside of the building would be painted black on the top "floor" to amplify its heating and thereby increase the thermal differential with the bottom "floor"; recall that the thermal differential is what drives any heat engine, so we are in the ironic position of painting part of a building black so as to make it cooler.
I am puzzled that increased airflow would work to cool ice as well as people. People are hotter than the surrounding air and can drink water, so more airflow means faster cooling. Somehow this effect works to preserve ice also, but I do not quite understand how, as increasing evaporative cooling for ice means losing ice faster. I have not done the physics to check how this would help keep ice around longer, but I don't think people would have done it if it did not work as a practical matter.
Further, your body also gets used to the heat. I have not lived in the Maryland tidewater for decades and my body misses being that hot in the summer; I now live in coastal Northern California, which almost never feels warm for someone who grew up where I did. To this day I hate air conditioning and it gives me headaches and I feel terrible in it. I will not hang out in a building that has air conditioning on to the point where I leave restaurants etc. (just last Friday made a friend leave a bar and go to another with me because it was air conditioned.) I even had my mechanic deliberately break the air conditioning in my last car so that if someone asked me to turn it on I could honestly say that it does not work; I insisted on not learning how he broke it so I could not fix it. In the SF Bay Area we have micro-climates: sometimes you can stand on the top of a hill in San Francisco where it is 65 degrees F and see with your eyes the top of Mount Diabolo 25 miles away where it might be 90 degrees F. In the summer I will check the temperature on the inland side of our local range of hills and many times, when the other side of the hills has been 15 degrees F warmer than my apartment, I have driven the 15 miles just to hang out in a parking garage outside and write code on my laptop (all the cafes are air conditioned). When I have sometimes left my car in the sun and I return to find it about 120 degrees F inside, I will just sit there and just enjoy it for a while before driving off. Again, you just get used to heat. My body just craves being really hot, especially for a few months in the summer. My favorite temperature is about 90 degrees Fahrenheit.